Consider some unlikely facts: The taller the man, the shorter his lifespan, on average. The more you daydream, the less happy you are. These are examples of inverse relationships, which often violate our expectations. We expect two factors to be linked. But instead of rising and falling in tandem, when one goes up the other comes down, making us sit up and take notice.

That was my reaction when I read about the inverse relationship between a leader's extroversion and that of his or her staff. A study to be published in June in the Academy of Management Journal reports that the more extroverted a leader is, the more effective he or she is with a passive work force. It's the reverse with an introverted leader: the more reserved the manager, the more successful with proactive employees.

"We have a prototype in mind that leaders should be extroverted," said Adam Grant, a management professor at the Wharton School at the University of Pennsylvania. But Professor Grant, along with co-authors Francesca Gino and David Hofmann, "wanted to go beyond people's impressions to see if groups with extroverted leaders actually perform better."

They do - as long as the employees simply follow orders. But when the staff is brimming with initiative, things can go off-track. That's because extroverted leaders "want that spotlight," Prof. Grant explained.

The researchers discovered this inverse relationship after sending questionnaires to managers and employees at 130 pizza franchises. They asked the managers to rate how extroverted they considered themselves, and asked employees how often they tried to improve procedures. Then the profitability of each store was tracked.

The study found that stores with passive staff and extroverted managers had profits 16 per cent higher than the national average. But stores with both a proactive staff and an extroverted leader struggled: Their profits dropped 14 per cent below the average.

"What extroverted leaders do well is they're energizing and assertive when setting a strategy," and this motivates employees who are dutiful followers, Prof. Grant explained. "But if you have a proactive work force, extroverted leaders feel more threatened, because one of the defining features of extroversion is the desire to seek out and attract attention."

Proactive employees need a leader who is open, receptive and a better listener, he said, "someone who seeks input, ideas and contributions from key employees and stakeholders. That's when acting more introverted can motivate employees to contribute more."

In a second, lab-based study, the researchers asked 163 university students, working in teams, to fold as many T-shirts as possible. Half the students in each team were confederates, instructed to stop the group after 90 seconds and say "I wonder if there's a more efficient way to do this?" In other teams, the confederates were instructed to simply follow the team leader's instructions.

To see if the team leaders' style could be changed, some were asked to read a passage about well-known, effective extroverts such as Jack Welch and Martin Luther King. The other team leaders read a passage citing Gandhi and Abraham Lincoln as examples of people whose reserved style helped them to empower others. Then the team leaders rated their own behaviour style; they were also assessed by their team. The researchers found that the assigned readings had an impact on the leaders' behaviour.

When the teams' performances were measured, the inverse relationship resurfaced. Those led by introverts folded 28 per cent more T-shirts when the workers showed initiative. Teams led by the extroverts folded more T-shirts when the workers were passive.

I asked Prof. Grant whether he expects his findings to hold up in more complex settings. "I suspect that our results would actually be stronger in more difficult and creative tasks," he replied. "Food delivery and production are contexts in which employee proactivity adds relatively little value, compared to settings in which proactivity can lead to the discovery or improvement of key products, processes or technologies."

We expect leaders to be command-and-control types, and most of them are. But it seemsprofitability is less about a leader's traits and more about the synergy between a boss's personality and the temperament of the staff.

Susan Pinker is a psychologist and author of The Sexual Paradox: Extreme Men, Gifted Women and the Real Gender Gap.

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